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--- pp:l09 [2020/04/25 19:21]
pdmatei
+++ pp:l09 [2020/04/25 19:31] (current)
pdmatei
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 . It is likely that your implementation will recompute (unnecessarily) the values $math[f(a), m, f(m), f(b)] in recursive steps. Write an alternative implementation which avoids this.
+. Consider a representation of maps (with obstacles as follows):
+<code haskell>
+l1="   #     "
+l2=" #   # # "
+l3=" # ### # "
+l4=" #     # "
+l5=" ####### "
+l6="         "
+data Map = Map [String]
+instance Show Map where
+  show (Map m) = "\n" ++ foldr (\x acc->x++"\n"++acc) [] m
+m = Map [l1,l2,l3,l4,l5,l6]
+type State = (Int,Int)
+</code>
+Write the function ''at'' which returns the value of the position ''x'',''y'' in the map:
+<code haskell>
+at :: Map -> Int -> Int -> Maybe Char
+</code>
+. Define a function which computes, for a given position, the list of valid //next positions// (a valid position is one that is on the map, and it is not a //wall//, i.e. a ''#''). Hint, use the list ''[(x-1,y-1),(x-1,y),(x-1,y+1),(x,y-1),(x,y+1),(x+1,y-1),(x+1,y),(x+1,y+1)]''.
+. Implement the type ''Tree a'' of trees with arbitrary number of children nodes.
+. Enrol ''Tree'' in class ''Functor'' (see classes), and define the function ''fmap''.
+. Write a function which takes a (possibly infinite) tree and returns the sub-tree where each branch is of length at most ''k'':
+<code haskell>
+take_t :: Integer -> Tree a -> Tree a
+</code>
+. Implement the infinite tree of valid positions, starting from an initial one. In this tree, paths represent trails exploring the map.
+<code haskell>
+make_st_tree :: Map -> State -> Tree State
+</code>
+. Implement the function ''toMap'' which //draws// a position on the map (using the character ''.'').
+<code haskell>
+toMap :: State -> Map -> Map
+</code>
+. Implement the tree of possible //trails// through the map:
+<code haskell>
+make_map_tree :: Map -> State -> Tree Map
+</code>